<ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">State a sequence of transformations that will transform the curve with equation $y={{x}^{2}}$on to the curve with equation $y=\frac{1}{4}{{\left( x-3 \right)}^{2}}$.</span></div><p style="text-align: right;">[2]</p></li></ol>
<p>A curve has equation $y=\mathrm{f}\left( x \right)$, where</p>
<p style="text-align: center">$\mathrm{f}\left( x \right)=\left\{ \begin{matrix}
1\mathrm{ for }0\le x\le 1, \\
\frac{1}{4}{{\left( x-3 \right)}^{2}}\mathrm{ for }1&lt;x\le 3, \\
0\mathrm{ otherwise}\mathrm{.} \\
\end{matrix} \right.$</p>
<ol class="i-list" start="2"><li><div class="list-item-content"><span class="list-item-text">Sketch the curve for $-1\le x\le 4$.</span></div><p style="text-align: right;">[3]</p></li><li><div class="list-item-content"><span class="list-item-text">On a separate diagram, sketch the curve with equation $y=1+\mathrm{f}\left( \frac{1}{2}x \right)$, for $-1\le x\le 4$.</span></div><p style="text-align: right;">[2]</p></li></ol>

State a sequence of transformations that will transform the curve with equation $y={{x}^{2}}$on to the curve with equation $y=\frac{1}{4}{{\left( x-3 \right)}^{2}}$.

A curve has equation $y=\mathrm{f}\left( x \right)$, where

$\mathrm{f}\left( x \right)=\left\{ \begin{matrix}
1\mathrm{ for }0\le x\le 1, \\
\frac{1}{4}{{\left( x-3 \right)}^{2}}\mathrm{ for }1&lt;x\le 3, \\
0\mathrm{ otherwise}\mathrm{.} \\
\end{matrix} \right.$

On a separate diagram, sketch the curve with equation $y=1+\mathrm{f}\left( \frac{1}{2}x \right)$, for $-1\le x\le 4$.

N2015 P1 Q5

N2015 P1 Q5

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